Extreme Value Theorem (EVT)
Read this topicExplanations 2
- Statement of the theorem Thm: If fff is continuous on a closed and bounded interval [a,b][a,b][a,b], then ∃ y∈[a,b]\exists \ y \in [a,b]∃ y∈[a,b] such that ∀ x∈[a,b],f(y)≥f(x)\f…
By Taras Kolomatski, Matt Superdock
- (Video) Extreme Value Theorem by learnifyable Here's a video by learnifyable explaining the Extreme Value Theorem.
By Alex Federspiel
Problems 2
- Let f:[0,3]→Rf:[0,3] \to \mathbb{R}f:[0,3]→R via f(x)=−2x2+8xf(x) = -2x^2 + 8xf(x)=−2x2+8x. The Extreme Value Theorem tells us that there exists y∈[0,3]y \in [0,3]y∈[0,3] such t…
- Let f:[0,2π)f:[0, 2\pi)f:[0,2π) via f(x)=3sin(5x)−4cos(3x)f(x) = 3 \sin(5x) - 4 \cos(3x)f(x)=3sin(5x)−4cos(3x). Does there exist y∈[0,2π)y \in [0, 2\pi)y∈[0,2π) such that ∀x∈[…